4 digits

Calculus Level 2

Sam fisher have accomplished a mission. But while leaving the area, he forgot the 4 digit door code. He can't open the door without the 4 digit code.

However, he got some clues:

  • The first digit is 2.

  • The second digit is ∫ 0 2 2 4 − 1 2 d x \displaystyle \int^2_0 \dfrac 24 - \dfrac 1 2 dx

  • The third digit is lim ⁡ x → ∞ 2 − x 4 − x \displaystyle \lim_{x \to \infty} \dfrac{2-x}{4-x}

  • The fourth digit is 2 2 0 + 6 \large 2^{2^0} + 6

What is the 4 digit integer?


The answer is 2018.

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

. .
Mar 15, 2021

The first digit is 2 .

The second digit is ∫ 0 2 2 4 − 1 2 d x = 0 \displaystyle \int ^ { 2 } _ { 0 } \frac { 2 } { 4 } - \frac { 1 } { 2 } dx = 0 .

The third digit is lim ⁡ x → ∞ 2 − x 4 − x = 1 \displaystyle \lim _ { x \to \infty } \frac { 2 - x } { 4 - x } = 1 .

The fourth digit is 2 2 0 + 6 = 2 1 + 6 = 2 + 6 = 8 { 2 ^ { 2 } } ^ { 0 } + 6 = 2 ^ { 1 } + 6 = 2 + 6 = 8 .

Hence, the code is 2018 \boxed { 2018 } .

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